In a variety of electronic circuit contexts, it is desirable to have available epitaxial layers of lattice-mismatched materails. For example, as known in the art, since silicon is an indirect bandgap semiconductor material, neither optical senders nor speedy and sensitive optical detectors can be made of silicon. Therefore, in opto-electronic circutis it is desirable to have an epitaxial layer of a different bandgap semiconductor--such as germanium (Ge) or a direct-gap Group III-V semiconductor like gallium arsenide--on a silicon (Si) substrate, with either optical devices, such as optical sender or optical detector elements or both, being integrated in the epitaxial layer, and with the bulk of the electronic data processing circuitry being integrated in the relatively low-cost silicon substrate. Moreover, in the case of date processing circuitry where purely silicon semiconductor integrated circuit transistors would operate too slowly, it is desirable to integrate some, but not all, of the transistors in single crystal gallium arsenide semiconductor, where transistors can operate faster, and to integrate the remainder of the transistors in single crystal silicon. In such cases, the more critical data processing calculatons--more critical in that the speed of these data calculations limit the overall speed of calculations--are allocated and routed to the transistors that are integrated in the gallium arsenide, whereas the less critical calculations are allocated and routed to the transistors that are integrated in the silicon. Thus, in such cases it is desirable to have single crystal gallium arsenide that has been epitaxially grown upon single crystal silicon to form a unified structure, the critical transistors being integrated in the gallium arsenide and the remaining transistors in the silicon.
On the other hand, because of the lattice mismatch between different semiconductor materials--e.g., about 0.22 Angstrom or about 4% mismatch between Ge and Si--during epitaxial growth, great stresses are unavoidably established in the region of the interface of epitaxial layer and substrate, whereby the epitaxial layer suffers in quality from such defects as lattice dislocations, so that transistors formed in the epitaxial layer do not operate properly, if at all. As the epitaxial layer is made thicker, the formation of lattice dislocation becomes more likely. For example, in order to grown upon a single crystal silicon substrate a dislocation-free epitaxial layer of Ge.sub.x Si.sub.1-x having a thickness of even as little as 100 Angstrom, the Ge content must be limited to a mole fraction x less than about 0.5, whereas a mole fraction x equal to unity (pure Ge) is desirable for optical elements formed in the epitaxial layer, and in prior art such a layer (with x=1) cannot be grown dislocation-free upon a silicon substrate regardless of how small the thickness of the layer is made. More generally, it is desirable to extend the thickness range of dislocation-free heteroepitaxial layers grown upon single-crystal substrates, such as commerically available semiconductor substrates like Si, gallium arsenide (GaAs), and indium phosphide (InP).